Production
situation PS‑1 represents a land‑use system with the least possible
analytical complexi­ty; all land qualities which can be influenced by a farmer
through irrigation and drainage, use of fer­tilizers, weeding and control of
pests and diseases are assumed to be optimum. The production calculated for
production situation PS‑1 is the highest production possible on a
farmer's field. It is the 'biophysical production potential'.

The biophysical production potential is determined by the solar radiation and
temperature du­ring the growing period and by the physio­logical characteris­tics
of the crop. Analysis of production situation PS‑1 is based on the same
principles as calculation of net biomass pro­duction for agro‑ecological
zoning but the procedure is dynamic and consi­derably more detailed.

The basic methods to calculate production potentials are described in Land use systems analysis by P.M. Driessen and N.T. Konijn (1992). Chapter 8 contains the formulas for PS1. The complete book can be downloaded here; to read chapter 8 (page 108 and following), please use the bookmarks in the PDF.

Photosynthesis

The fundamental process behind plant growth is assimilation, i.e. reduction of atmospheric CO2 to carbohydrates, (CH2O)n. Assimilation requires energy; it is a unique capability of green plants that they can capture solar energy and use it in assimilation:
CO2
+ H2O + solar energy ‑‑> 1/n(CH2O)n
+ O2 (1a)

Conversion
of (CH2O)n to CO2 and H2O
occurs also. This process is known as respiration; it releases chemical
energy which can be used by the plant.

Pathways of photosynthesis

The rate of assimilation under conditions of light saturation and op­ti­mum temperature differs among plants. Three different pathways of photosynthesis exist of which two have practical importance.

one group of plants produces C3H6O3 as the first assimilate; plants in this group are called C3‑plants after the length of the carbon chain of the first assimilate

plants in the second group produce C4H8O4 as the first assimilate; they are the C4‑plants.

An important difference between C3‑plants and C4‑plants is that respiration in the sunlit photosynthetic organs (photorespiration) is considerable in C3‑plants and negli­gible in C4‑plants.

Losses of assimilates incurred in photo­res­pi­ration increase with temperature and
intensity of light. This has practical consequences.

C4‑plants make more efficient use of intercepted
solar radiation than C3‑plants at high light intensity (there is little
dif­ference at low light intensity)

The
amount of solar energy at the outer extremity of the atmosphere varies with the
latitude of the site and the time of year. Approxi­mately half the total
global radiation is photosynthetically active radiation (PAR). The
trans­parancy of the atmosphere determines how much radiation reaches the
canopy. Light response curves relate irradiance with gross assi­mi­lation.
Light response curves are described by only two parameters.

-light use efficiency at low light intensity
(EFF)

-maximum rate of assimilation (AMAX).

AMAX
(kg ha-1 h-1) is the gross rate of assimilation at light
saturation; AMAX is co-determined by photorespiration and is much greater for
C4‑crops than for C3‑crops. AMAX is strongly temperature‑dependent;
EFF decreases by only 1% for every degree of tempe­ra­ture increase in C3‑plants,
and even less in C4‑plants. For practical purposes EFF is a constant with
a value of some 0.5 kg ha-1 h-1/J m-2 s-1
(de Wit et al., 1978).

The above figure presents light response curves of maize leaves at several tempera­tures.
Observe that ambient temperature has a much more pronounced effect on AMAX (the
plateau) than on EFF (the initial angle of the curve).

It
is unfortunate that curves like those Figure 1 cannot be used to describe
the assimilatory potential of field‑grown crops. It appears that the
photo­synthetic activity of plant leaves is influenced by the radiation and
temperature to which the leaves were exposed in the past. It is for this reason
that the AEZ team defined crop‑adaptability groups with different
AMAX‑to‑tempera­ture relations. The response curves in Figure 2
resemble those used by the AEZ team (FAO, 1978).

Note that Figure 2 is a simplification; the optimum temperature
for assimilation by a C3‑crop cannot be a steady 18 oC in cool
climates and 27 oC in the tropics if it is co‑determined by
the temperatures to which the crop was actually exposed.

Therefore actual assimilation will be calculated as a fraction of assimilation
at a reference temperature (Tref). Tref is the temperature to which the
assi­mi­lating plant 'got used'; it is tentatively defined as the weighted
average of the daytime tem­peratures (Tday) over the past 10
days, with a mini­mum of 15 oC and a maximum of 30 oC.

Curves I and II in Figure 2 suggest the following AMAX‑to‑temperature
relation for C3‑crops.

AMAX = 1.8 * Tref - 0.15 * (Tref - Tday)2
(8.2a)

Approximate
AMAX‑to‑temperature relations for C4‑crops are obtained by
dividing response curves III and IV in Figure 2 in three linear trajecta.

The MaximumAssimilationAlgorithm is just one of the algorithms out of a whole group of algorithms that were developed for PS-1 and PS-2. For an overview of all implemented algorithms, see nl.itc.cropspecificproductionlevels package-summary.

Some algorithms were grouped e.g. SunlightAlgorithm, CropGrowthAlgorithm and OrganGrowthAlgorithm. One algorithm may call another algorithm, etc.

To run the whole simulation for a single point for a complete growing season, you can use ProductionAlgorithm.

The
equivalent daytime temperature (Tday) is found by integrating
the temperature curve between sunrise and sunset (M. v.d. Berg, pers. comm.).
It is assumed that the maximum tempera­ture occurs at 14.00 hrs and the lowest
temperature at sunrise.

Tday = Tmid + (SUNSET - 14) * AMPL * sin(AUX) / (DL *
AUX)
(8.3.1)

with

Tmid = (Tmax + Tmin) /
2
(8.3.2)

AMPL = (Tmax - Tmin) /
2
(8.3.3)

SUNRISE = 12 - DL /
2
(8.3.4)

SUNSET = 12 + DL /
2
(8.3.5)

AUX = PI * (SUNSET - 14) / (SUNRISE +
10)
(8.3.6)

where

Tmax
is maximum daily temperature (oC)

Tmin
is minimum daily temperature (oC)

DL
is daylength (h d-1)

PI
is a constant (PI = 3.14159).

The
equivalent night temperature (Tnight) is found by integrating
the temperature curve between sunset and sunrise.

Tnight = Tmid - AMPL * sin(AUX) / (PI -
AUX)
(8.3.7)

The
daylength (DL) is a function of the day in the year and the latitude of
the site (de Wit et al., 1978).

DL = 12 * (PI + 2 * asin(SSCC)) /
PI
(8.4)

with

SSCC = SSIN /
CCOS
(8.4.1)

SSIN = sin(LAT * RAD) * sin(DEC *
RAD)
(8.4.2)

CCOS = cos(LAT * RAD) * cos(DEC * RAD)
(8.4.3)

DEC = -23.45 * cos(2 * PI * (DAY+10) /
365)
(8.4.4)

where

RADis a conversion factor (degree to radian; RAD =
PI / 180)

LAT is latitude of the site (degree)

DEC is declination of the sun (degree)

DAY is Julian day number on the northern hemisphere, or
Julian day number plus or minus 182 on the southern hemisphere.

Note
that Equations 8.2, 8.3 and 8.4 relate AMAX to a few readily
available data, viz. latitude of the site (LAT, in degree), Julian day number
(DAY), and daily maximum and minimum temperatures (Tmax and Tmin).

Sunflower case

Question 1

Check the information on crop photosynthetic mechanism.
What is the crop type for sunflower: C3 or C4?

C3
C4

Question 2

In case 1 the reference temperature is 15°C and daytime temperature is 24°C and in case 2 the reference temperature is 15°C while the daytime temperature is 14°C. Which case is better for sunflower production? You may run the MaximumAssimilationAlgorithm for both cases to find out.